On the Methodology for Studying the Operating Modes of Bar-Type Earth-Cutting Machines
Abstract Generated abstract
This paper develops a methodology for studying operating modes of bar-type earth-cutting machines, using experiments in thawed sandy soil as a basis for later winter and frozen-soil investigations. The authors record torque, rotational speed, feed force, and feed speed to relate power consumption, cutting-chain speed, feed speed, chip thickness, and tractive force. The results indicate that idle chain-pulling power increases linearly with chain speed, while cutting energy decreases with increasing chip thickness up to an optimum range and is affected by a critical minimum cutting speed. The paper proposes criteria for selecting optimal speed ratios for a given power, derives relations for feed force and maximum feed rate, and identifies unresolved dynamic load oscillations in the transmission that require further study.
Full Text
Toward a Methodology for Studying the Operating Modes of Bar-Type Earth-Cutting Machines
O. D. Alimov, I. G. Basov, D. N. Malikov, E. I. Lisovskii
To develop a methodology for studying the operating modes of earth-cutting machines under winter conditions, similar investigations were carried out in cutting thawed soil. The results of these investigations will help avoid errors when conducting experiments under winter conditions, and also have independent significance in evaluating certain parameters of earth-cutting machines.
The experiments were carried out with the aim of determining:
a) the dependence of the feed force on the cutting speed;
b) the dependence of the energy intensity of the cutting process on the cutting and feed speeds;
c) the optimum operating modes of an earth-cutting installation for a given engine power;
d) the loads in the transmission of the working element under different operating modes of the earth-cutting installation.
To obtain the above-indicated dependences during operation of the earth-cutting machine, four parameters were recorded simultaneously on an oscillogram: the torques on the shafts of the engine \(M_{\mathrm{eng}}\) and of the cutting-part reducer \(M_{r}\), the shaft rotation speed \(n\), and the feed force \(F_{\mathrm{p}}\). In addition, during the experiments the feed speed \(v_{\mathrm{p}}\) was determined.
- Power expenditures during idle pulling of the cutting chain were determined as follows. The bar was removed from the slot and set in a horizontal position. The cutting chain was set in motion at various speeds, and the machine moved with the minimum feed speed \((v_{\mathrm{p}} = 13\ \text{m/hour})\). At the same time the principal force parameters were recorded on an oscillogram.
The dependence of the power expenditure on the speed \(v_{\mathrm{r}}\) of idle pulling of the cutting chain may be considered rectilinear (Fig. 1) and expressed by the empirical equation
\[ N_{\mathrm{p}} = 2.8\,v_{\mathrm{r}},\ \text{hp}. \tag{1} \]
On the other hand, the power on the driven shaft of the cutting part can be determined by the known formula
\[ N_{\mathrm{p}} = \frac{P \cdot v_{\mathrm{r}}}{75\eta_{\mathrm{r}}}, \tag{2} \]
where \(\eta_{\mathrm{r}} = 0.9\) is the efficiency of the cutting-part reducer;
\(P\) is the pulling force of the chain, kg.
Solving (1) and (2) jointly, we obtain
\[ P=\frac{75\cdot 2.8\cdot v_{\mathrm{p}}\eta_{\mathrm{p}}}{v_{\mathrm{p}}} =75\cdot 2.8\cdot 0.9=190\ \text{kg}. \]
Thus, for a bar-type operating member of the “Ural-33” type with a length of 2 m, the magnitude of the idling tractive force of the cutting chain does not depend on changes in the speed of motion of the latter within the range \(0.4—5.6\ \text{m/sec}\).
From Fig. 1 it follows that the power expended on idly pulling the chain increases with increasing chain speed and, at \(v_{\mathrm{p}}=5.6\ \text{m/sec}\), reaches 16 h.p. Hence it may be concluded that it is inexpedient to adjust low-power earth-cutting machines to high cutting speeds, since the specific weight of harmful resistances in such machines will be large.
Fig. 1. Dependence of the power consumed by the cutting part on the idle speed of the cutting chain
2. Power expenditures in the process of cutting soil were determined at seven different cutting speeds within the range \(0.44—5.6\ \text{m/sec}\) and six feed speeds within the range \(13—125\ \text{m/h}\). The combination of the above cutting and feed speeds amounted to more than 30 different operating modes. On the basis of the results of the investigations, dependences were constructed for the power consumed by the cutting part on the feed speed for various cutting speeds (Fig. 2).
Analyzing these dependences, the following conclusions can be drawn.
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At a constant cutting speed, an increase in feed speed leads to an increase in power consumption.
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At an unchanged feed speed, the power depends on the cutting speed, and this dependence is different at different feed speeds.
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The minimum power expenditures at a given feed speed are attained at a definite cutting speed.
3. Energy intensity of the cutting process was determined by the formula
\[ q=\frac{0.736\cdot N_{\mathrm{p}}\eta_{\mathrm{p}}}{H_{\mathrm{sh}}v_{\mathrm{p}}},\ \text{kW}\cdot\text{h}/\text{m}^{2}, \tag{3} \]
where \(H_{\mathrm{sh}}=1.5\ \text{m}\) is the depth of the slot cut by the bar-type operating member, with a width of \(0.14\ \text{m}\).
If the experiments are carried out using bars of different thickness, the energy expenditures must be referred to a cubic meter of destroyed soil, i.e., the slot width must also be included in formula (3).
The energy intensity of the cutting process depends on the cutting and feed speeds, since for a given design of the operating member their ratio determines the thickness of the chip removed by the cutter:
\[ h=\frac{b\cdot t\cdot z_{\mathrm{k}}\cdot v_{\mathrm{p}}}{3600\cdot z v_{\mathrm{r}}},\ \text{mm}, \tag{4} \]
where \(b\) is the number of cutting lines;
\(t\) is the chain pitch, mm;
\(z_k\) — number of cams in the cutting chain;
\(z\) — number of cutters in the cutting chain.
Figure 3 presents the dependences \(q=f(h)\), from which it follows that, as the chip thickness increases from 0.5 to 8–15 mm, the energy consumption of cutting decreases. A further increase in \(h\) practically does not change
Fig. 2. Dependence of the power consumed by the cutting part on the feed speed of an earth-cutting machine when cutting unfrozen sandy soil at cutting-chain speeds:
1 — 0.44 m/s; 2 — 0.74 m/s;
3 — 1.4 m/s; 4 — 2.4 m/s; 5 — 3.3 m/s; 6 — 4.5 m/s;
7 — 5.6 m/s
the value of \(q\). At cutting speeds in the range of 1.4–5.6 m/s, the energy consumption is determined by the chip thickness and is practically independent of the cutting speed. At cutting speeds below 1.4 m/s, the energy consumption depends not only on the chip thickness but also on the cutting speed. Reducing the cutting speed at one and the same chip thickness increases the energy consumption. This can be explained by the fact that, as visual observations show, at low cutting speeds not all the soil lifted from the slot leaves the cutting chain. The lower the cutting speed, the more soil is drawn back into the chain. At considerable cutting speeds, after the cutters and cams leave the slot, the soil falls from them under the action of the vibration of the cutting chain and of the centrifugal forces that arise as the chain passes around the driving sprocket of the bar. Consequently, from the standpoint of unloading the teeth and chain links from soil, there exists a certain minimum critical cutting speed below which the cutting process is accompanied by an increase in energy consumption. The magnitude of the critical cutting speed is apparently determined mainly by the properties of the soil and, to some extent, by the design of the cutting chain. For unfrozen sandy soil it proved to be approximately 1.4 m/s; for clayey soil (especially wet soil) [[unclear: word]], it will probably be considerably higher, and for frozen soils, possibly lower.
4. The tractive force of the crawler propulsion unit of the earth-cutting installation was measured under various cutting regimes. Based on the experimental results, the dependence of the tractive force \(F_{\text{t}}\) on the chip thickness \(h\) was constructed (Fig. 4). It is seen from Fig. 4 that the tractive force is the sum
\[ F_{\text{t}} = F_{\text{x.x}} + F_{\text{b}}, \]
where \(F_{\text{x.x}}\) is the tractive force of the tracks during idle movement of the earth-cutting installation over a horizontal site and, in our case, is \(320\ \text{kg}\);
\(F_{\text{b}}\) is the feed force of the bar into the ground.
With some approximation one may take
\[ F_{\text{b}} = k \cdot h, \]
where \(k\) is a proportionality coefficient depending on the physicomechanical properties of the soil, as well as on the dimensions and design of the cutting member. For our case, i.e., when cutting in unfrozen sandy soil a slot \(1.5\ \text{m}\) deep with the bar-type working member of the “Ural-33” type, \(k = 24\ \text{kg/mm}\).
Then
\[ F_{\text{t}} = F_{\text{x.x}} + kh. \]
Knowing the tractive force at a known travel speed of the earth-cutting machine, one can determine the power required to feed the working member.
Fig. 3. Dependence of the energy intensity of soil cutting on the thickness of the chip cut by an individual cutter at cutting speeds: \(1\)—\(1.4;\ 2.4;\ 3.3;\ 4.5;\ 5.6\ \text{m/s}\); \(2\)—\(0.74\ \text{m/s}\); \(3\)—\(0.44\ \text{m/s}\); solid line—by power at the shaft of the drive sprocket; dashed line—by power at the motor shaft.
5. At a constant slot depth and with fixed design parameters of the working member and its transmission, the energy intensity, according to formula (3), is proportional to
\[ \frac{N_{\text{p}}}{v_{\text{p}}}, \]
while the chip thickness (2) is proportional to
\[ \frac{v_{\text{p}}}{v_{\text{b}}}. \]
Consequently, the dependence \(q = f(h)\) may be regarded as a function
\[ \frac{N_{\mathrm r}}{v_{\mathrm p}}=f\left(\frac{v_{\mathrm p}}{v_{\mathrm r}}\right), \]
reflecting the interrelation between the power consumed by the bar and the cutting and feed speeds.
In this connection it may be considered that the most economical cutting mode is ensured by such a ratio \(\frac{v_{\mathrm p}}{v_{\mathrm r}}\) at which the energy consumption will be minimal. If the minimum value of the energy consumption \(q_{\min}\) occurs at chip thickness \(h_{\mathrm{opt}}\), then, for a given power \(N_{\mathrm r}\), the maximum feed rate
Fig. 4. Change in the engine tractive force as a function of chip thickness
Fig. 5. Influence of the speed of motion of the cutting chain on the nature of the load on the transmission of the working member
\[ v_{\mathrm{p.max}}=\frac{0.736N_{\mathrm r}\cdot\eta_{\mathrm r}}{H_{\mathrm c}\cdot q_{\min}} \tag{5} \]
will be attained under the condition
\[ \frac{v_{\mathrm p}}{v_{\mathrm r}}=\frac{3600\cdot z}{b\cdot t\cdot z_{\mathrm k}}\,h_{\mathrm{opt}}. \tag{6} \]
For a given speed \(v_{\mathrm p}\), the required minimum possible cutting power is determined from expression (5), provided condition (6) is observed.
For the given working member and soils, the minimum energy consumption of cutting, which is attained at one and the same chip thickness (\(h_{\mathrm{opt}}=\mathrm{const}\)), the indicated optimal ratio of speeds \(\frac{v_{\mathrm p}}{v_{\mathrm r}}\) is a constant quantity and must be maintained independently of the absolute values of \(v_{\mathrm p}\) and \(v_{\mathrm r}\). The only exception to this rule is the circumstance that the cutting speed must not be lower than the critical value \(v_{\mathrm{r.cr}}\), as was stated above. The critical cutting speed determines the lower limit of the optimal feed rate
\[ v_{\mathrm{p.min}}=v_{\mathrm{r.cr}}\frac{3600\cdot z}{b\cdot t\cdot z_{\mathrm k}}\,h_{\mathrm{opt}},\ \mathrm{m/h}, \]
below which it is impossible to provide the machine with the optimum operating mode.
- In studying oscillograms recording the torques on the shaft of the gearbox of the cutting part \(M_r\) and on the motor shaft \(M_{\mathrm{dv}}\), the following was observed.
The torques \(M_r\) and \(M_{\mathrm{dv}}\) do not remain constant during operation of the earth-cutting unit in a specified mode. Their values vary synchronously and periodically upward or downward from certain constant mean values.
At one and the same cutting speed, the frequency \(\omega_A\) and amplitude \(A_m\) of the oscillation of the torque \(M_r\) remain approximately constant, or \(\omega_A\) increases slightly while \(A_m\) decreases as the feed speed increases.
The number of oscillations of \(M_r\) occurring during one revolution of the shaft of the gearbox of the cutting part, i.e., the ratio
\[ \frac{\omega_A}{n_r} \]
decreases with increasing cutting speed (Fig. 5). The pulsating character of the motion of the cutting chain is due, above all, to the kinematics of the “sprocket—chain” system, as well as to the periodic engagement of the cutters in the cutting process. In this connection, it would seem that the oscillation frequency \(\omega_A\) should change in proportion to the cutting speed, i.e., the ratio
\[ \frac{\omega_A}{n_r} \]
should be constant. In fact, however, we have the opposite picture. Consequently, the oscillatory character of the load described is determined by certain additional factors that must be identified.
The change in amplitude \(A_m\) as a function of cutting speed has a wave-like character. The maximum values (5.2 and 4.5 kg·m) correspond to cutting speeds of 2.4 and 5.6 m/sec. The relative value of the oscillation amplitude of \(M_r\), i.e., the ratio
\[ \frac{A_m}{M_r}, \]
also varies in a wave-like manner as a function of cutting speed, reaching maximum values (0.53 and 0.45) at cutting speeds of 2.4 and 4.6 m/sec.
To clarify the dynamic phenomena described above in the transmission of the bar-type cutting member, it is necessary to carry out more thorough investigations.
Conclusions
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In evaluating the expenditure of power on cutting soils by a bar-type working member, it is necessary to take into account the fact that the power consumed in the idle displacement of the cutting chain is directly proportional to the speed of its motion and, at high speeds, reaches considerable values. The force of idle pulling of the cutting chain, however, depends only on the design parameters of the working member and does not change as a function of the speed of motion of the cutting chain.
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The power expenditures in cutting soil and the energy intensity of the cutting process depend on the speeds of chain motion and feed of the working member, as well as on the physicomechanical properties of the soils. In this connection, in order to determine the optimum modes for cutting frozen soils of various physicomechanical properties, it is necessary to determine the optimum ratio
\[ \frac{v_{\mathrm{p}}}{v_{\mathrm{r}}} \]
or the chip thickness. In addition, at constant thick-
chip thickness it is necessary to determine the minimally possible critical cutting speed, below which the energy consumption of cutting increases.
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In studying the operating modes of an earth-cutting unit, it is necessary to determine the dependence of the engine tractive force on the chip thickness. This will make it possible to identify both the tractive force required for idle movement of the earth-cutting unit and the feed force of the working element at the face.
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The optimal operating modes of a bar-type working element must be determined from conditions (5) and (6).
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Detailed studies must be carried out of the dynamic phenomena arising in the transmission of a bar-type working element when cutting frozen soils.